Manuel geogebra 6.0 pdf

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Manuel geogebra 6.0 pdf

Manuel geogebra 6.0 pdf.

GeoGebra Manual Boxplots (, , ) creates a raw data with existing box plot. Its vertical position in the coordinate system is influenced by yabstand and "Yscalation" factor, which adjusts the height adjusted. Example: Boxplots [0, 1, {} 2,2,4,4,5,5,7,7,8,8,8,9] Boxplots (, , , < Q1>, , , ) Creates a box-plot with the statistical data shown in the interval between the initial value and the final value. Boxplots (, , , ) This allows you to be displayed as "X" instead of being included in the box-plot. "Outliers" are data that are below Q1 - 1.5 * [Q3 - Q1] or higher Q3 + 1.5 * [Q3 - Q1] (see also IQR). Boxplots (, , , , ) This displays a box plot with the data of a frequency table. CAS View User Interface By default, the Cas View is opened next to the Graphics View. Depending on which of the two theses Views is active, Eithher Cas View toolbar or the Graphics View toolbar appears at the top of the GeoGebra window, with Beito / Redo buttons in the top right corner. View Cas Cas Cas View is part of the perspective, although you can change the GeoGebra user interface layout to suit your needs. Creating Mathematics Items The CAS View allows you to use GeoGebra CAS (Computer Algebra System) for symbolic calculations. It is composed of cells of a field input and output in the upper part of the bottom of the display. You may use thesis input fields in the same way as the normal input bar, with the following differences: You can use any unassigned variables value. = Used for equations and: = for assignment. This means that input A = 2 Will Not assign the value 2 to a. See the section on assignments for details. The multiplication is marked explicitly. While in the insertion bar is possible to use either is valid A (B + C) and A * (B + C) for multiplication, In Cas display only A * (B + C). Shortcut keys for direct input in The Cas View desktop version of GeoGebra The following Keyboard shortcuts help you to evaluate or control the entry. Note: instead of using the keyboard shortcuts Thesis, you can then use the corresponding tools of the corresponding toolbar. Enter: Value your input. Notes: The assignments are always evaluated, for example, A: = 5 can suppress any output with a semicolon at the end of your input, for example, A: = 5; You can use the: = write mode for assignments, for example BA: = 5, A (N) ?: = 2n + 3 free a name: Delete Use [B] in order to free up a variable name again . REDFINE a variable or function: you can Rudefine a variable or function, but it is necessary to do so in the same cell, OTHERWISE wants to be treated as a new variable and renamed automatically. Variables and functions are always shared between the CAS view and other views if possible. For example: if we define B: = 5 in La Cas View, then it is possible to use B in all other GeoGebra views. If you define a (x) Function F = X ^ 2 in another view, you can then use this function in the view cas. NOTE: Output wants Always Be Just The After The Expression: =, for example if you type B: 5 = Output wants to be 5. Note please, that for clarification actualy BA: will be displayed = 5. You can write equations using the simple equal sign, for example, 3x + 5 = 7. arithmetic operations: it is possible to perform arithmetic operations of equations, which is useful for the resolution of equations Example: (3x + 5 = 7) - 5 subtrae 5 on both sides of the equation. Extraction One side: You can extract or left right side of an equation using the Leftside [] and Rightside [] commands. Example: Leftside [3x + 5 = 7] Returns 3 x + 5 and rightside [3x + 5 = 7] Returns 7 Riga You Can References Return Other Rows in CAS View in two ways: Static Row Row Copy the output and will not be updated if the reference line is subsequently changed: Copy the previous output. # 5: Copy the output of the line 5. Dynamic line references insert a reference to another line instead of the actual output and then you will be updated if the reference line $ is subsequently modified: insert a reference to the output previous. $ 5: Inserts a reference to the Riga 5 CAS Commands GeoGebra output also offers a wide range of CAS commands that can be used to create objects in the Cas. Just start typing the name of a command in the input and geogebra field will offer you a list of commands that match your input. Note: For a complete list of commands, see the CAS command section. Note: From GeoGebra 5.0 onwards, the CAS view supports the exact versions of some geometric controls. CAS View Toolbar The CAS toolbar displays a range of CAS tools that allow you to evaluate the input and perform calculations. Just enter your input and select the corresponding CAS tool later to apply it to your input. Tip: In GeoGebra Classic 5 you can select part of the input text to apply only the operation to this selected part. This function is not available in classic 6 at the moment. Note: For a complete list of tools see CAS tools. In the geogebra desktop version you can right-click (MacOS: Ctrl-click) on a row header to show a shortcut menu with the following options: Insert above: insert an empty line above the current one. Insert below: insert an empty line under the current one. Delete Riga: Delete the contents of the current line. Text: Switch between the current result and a text showing the current result contained in the line, which allows the user to enter comments. Copy as a latex (geogebra desktop): copy the contents of the current line to the clipboard of your computer, allowing you to paste the content eg In a text object. Note: To copy the most of a CAS line as in Latex, select the desired lines with CTRL-Click (MacOS: CMD-click), then right-click (MacOS: Ctrl-click) on the Riga header and select copy as a latex. In the geogebra desktop version you can right-click (macos: ctrl-click) on a CAS output cell to show a shortcut menu with the following options: Copy: Copy the contents of cells on Notes of your computer. Then, rightclick on a new cell to show the Pasta option. Copy as a latex: Copy the contents of the cell in latex format on your computer's clipboard, then can be glued to a text object or a latex editor. Copy as LibreOffice Formula: Copy the contents of the cell in LibreOffice formula format to your computer's clipboard, then can be glued in a text processing document. Copy as Image: Copy the contents of the cell in PNG format on your computer's clipboard, then can be glued in an image object or in a text processing document. Displaying mathematical objects The Cas View style bar provides buttons to change the text style (Bold and Italics) and color display a virtual keyboard (geogebra desktop) Displays additional views in the GeoGebra window (Web App and Tablet GeoGebra) which Show CAS objects in the graphic view in the CAS view, the icon to the left of each line shows the current visibility status (shown or hidden) of the object defined in it (when possible). You can directly click Little Show / Hide the object icon to change the visibility status of the object in the graphic view. From the Geogbe manual, all They will include the latest bugfix accessories and translation updates. Versions are not simultaneous on all platforms and not all platforms will receive all versions (online and classic 5 will often receive a previous version) 6.0.6xx.0 (XXH August 2021 Build, not released) CAS: Correction to resolve ( 3 * SQRT (X + 4) 0) CAS: correction to resolve (SQRT (ABS (X ^ 2-25) +25) = ABS (x + 4) +4 ) Classic 5: Add Alternative Solution for Grande Sursuite: CAS, 3D, Geometry added CAS: improvement for eg. TRIGEXPAND (SIN (X) SIN (X / 3)) CAS: Take () Command Implemented SLOPEFIELD () - Option for arrows Adding symbolic input boxes: Keyboard suitable for the object Type of objects Symbolic input boxes: Type the names of the Greek letters repair directly for the numerator / denominator so denominator () will always be positive classic 6: bugfix to reorganize views x ^ (- (1/3)) tracked correctionynew command commands sustainll (, , ) and divide (, ) correction for playsound () fix for formutatext ("omega") correction for dialog boxes in the safari correction for formutatext (Vector) Fix for Google Drive IntegrationFixFix for the probability calculator (including the use of New Editor) Show placeholder for SuperScript / Informpresses / Lessons / Vectors / Matrices / etc. Correction for Korean Characters "doubled" Classic 5: correction for scroll wheel / touchpad on certain fixing devices for missing brackets in Algebra View for Translate (Function) Classic 5: Fix for missing settershey position: fix passes Passe from the Classic 5 Context menu: Double-click .GGBB file with Unicode file names files (eg Greek, Chinese) Works (full needed reinstallation) New text text alignment syntax (, , , , , ) CAS: correction to resolve ({tan (58 ? ?) = s / (50-t), tanning (47 ? ?) = s / t}, {s, t}) (graft bu g) cas: correction for integral ((exp ((((( (((- (x ^ 2)) / ((SQRT (((1-1 / 10))) ^ 2))), X, -1.17) (Internal (internal for about response) CAS: fixes for Integral (sqrt (tanh (x))), LimitBelow (floor (x), 1), Solve ({x ^ 2 + 2 * x * AA ^ 2 = -32, -3 * x ^ 2-2 * x * y + 3y ^ 2 = 32}, {x, y}), length ({(1,2,3), (4,5,6)}), solve (22044 = 6000 +264 * ((x + 1) ^ (60) -1) / (x) * (1) / ((x + 1) ^ (60)) + 7000 * (1) / ((x + 1) ^ (60))), limit (SINA ? (x) + What ? (x), x, a) | X | 0.8 == ^ | X | ^ (4/5) for the improvement Simplification (inequality) to fix the leakfix memory RandomPointIn () Intersect (, , , ) working for 3D curves "Use text as the caption" to allow dynamic captions for BoxesCAS input: RemoveUndefined () and IsInteger () implementedfix for ggbApplet.reset () fix for dropdowns not close on improvements click to paste in Algebra LaTeX input and boxes text new RemovableDiscontinuity () command for rational functions (even for previews) Notes: new tool table Editor: export to SVG, evalLaTeX () added, event for / focus lost added Chrome: copy image to clipboard workingfix for Inverse correction polygons to \ left \ langlefix for printing, for example, f (x) = ln (44) 3D: correction to rotate the view on touchlog (x) now gives log_10 (x) does not ln (x) correction for example, sin (x) ^ Cos (x) extra parameter added toggbApplet. getValueString ( "f", false) to make sure that the output is not localized correction sliders with 1? ? ? increment3D: new tool Surface graphics revolution make complex * complex works again correction \ correction in input boxes to Polygon (a, B, 3, airplane) when a and B are 2D points Notes: new complex instrument equation I visualized better in boxes and LaTeX textsDelete tool will not be! Cancel fixed objects in Activitiesbetter parsing of expressions without explicit multiply for example f (p, q) = sin (pq) correction for sometimes input boxes disappearing of new button of the edges color parameter set for example, "buttonBorderColor" "# FF00FF" graphic: length (list) to work again graphics: Equation shown by the line (a, B) again Boxes symbolic operation input for conic, implicit curves and quadrics now built with GWT 2.9 Android bug fix with undo (R8 compiler bug) Classic 6: correction to reopen settings (mostly iOS) Classic ing 6: make sure random numbers are not updated when CAS is loaded for fix angle is not shown when it's by Element (list 1) Suite (beta): now calculator remove unnecessary API callsClassic 5: "applied model" will also apply default styles for correcting existing objects for symbolic input boxes that disappear on t ouch correction for LaTeX ( "\ Rho") JavaScript preserved listeners a redefine GeoGebra 6: Correction installation where user name contains a fix space for Input Box eliminated in full screen button improved plotting for example ln (x) bugfix to draw grid with "only positive" axis better parsing of expressions without brackets for example sinsinsinx Classic 6: parenthesis added when typed after the name of the PI function replaced by I in the 3D input boxes Calculator: shutter button in mode AR Android 10 : in-line savings bug fixfix with numbers being turned into sliders Classic 5: fix bug with dragging down listsClassic: fix for the native keyboard appearing on iOS App 13.3.1 CAS: sliders and classical vectors work: correction example ggbApplet.evalCommand ( "$ 1: f (x) ? ? x ^ 2") make sure InputBox1 + "" and LaTeX (InputBox1) work properly fix for undo / redo with the simbol input boxes ici (not symbolic) input boxes linked to numbers now show only the numeric keyboard on Android / iOSmake safe online Exit indicated for Fitline () etc. New Web: correction for # and ? ? ? Android: correction keyboard closure problem on HTC Phonesgraphing: same in question and non-exam (construction features removed) more symbolic input security improvements (including vectors And the type cannot be modified by entering the syntax "bad") bugfix: ggbapplet.setfixed () do not trigger more onupdate script randomelement ({1 / 2.1 / 3.1 / 4}) works Betterfix location for LATEX captions up more symbolic input control boxes security improvements (including column vectors, fix to resize the problems and syntax errors maintained) bug fixes with always "locked" objects, as defined bug fix with background not be redesigned to the correction size properly With input boxes grabbing a response from another BoxHTML5 input: Fix Bug with Tracegraphing Calculator: Measurement, transformation and construction Controls and tools disabled Most symbolic entrance security improvements (between whose modification of matrices, lines and aircrafts) Classic 6: Fix problem "Double name" in the editor spreadsheet: "Preventfocus": False Fix option added for Isinregion () in Websimplenew command casloaded () improvement for random numbers updated on Redefinition (for example, when the content input of the change changed) - random numbers should be defined in their "own object" to take advantage of Thisclassic 5: correction for ggbapplet.registeraddlistener () Classic 6: correction for es setperspective ("s") symbolic input boxes work for example f (x, y) input boxes are empty rather than show? For undefined Geo tied iOS 3D: Correction for crashing on small screens (eg type X) Alignment option for input boxes CAS Calculator: plus added commands: Invert (), nSolutions (), sequence (), reduceprowechelonoform ( ), reserve (), sum (), transpose (), eliminateondefiniti (), tangent () CAS Calculator: corrections for example f (x) = cas app: first official output select input content of the package option "symbolic "for input containers FIX Rounding in input Boxesgeogebra 6: / for the overturned bar (eg Dutch keyboards) Correction for NAN in the input boxes, instead OFA PDF Export Background image correction for / tracks correction for point (function , cursor) when the function is defined corrected for the problem with input? Non-update boxes 2Make Numbers Certain numbers from zero-zero imaginary part are recharged correctly Editor: Improvement for sin? (x) Max polynomial limit at 1000 (affects ES coefficients () command) Android: 44 bit android devices support: Better sign-in method (for Google) Graphics: Make sure the DY / DX button uses NDER ivatives () non-derivative () Classic 6: Settings -> Algebra -> Missing Increment Classic 6: Fix the support for Raspberry PI 4 for The variable function of change in sequence (integral (F, A, B) (with the work in 3D View!). .. Android: Google Fix Login (from V547) GeoGebra 6: Chinese: The commands can be typed in Chinese or Englishfix attachcopytoview () for rays cas: fix for example simplify ((x ^ 2 + 2 * x + 1) / ((x + 1) ^ 8)) 3d: correction by surface () chromeos: geogebra classic now a packaged AppClassic 5: correction by JavaScript error ("Java.lang.String") 3D: CO DRESSING EXTRESSION FROM THE POLIGON CAS: Correction for Solutions (x ^ 2 = A) Correction for Horizontal Panning Glitchcas View: correction to resolve (8 / (P ^ (- 4000 * x)) = 6, x) and integral (sqrt (x + SQRT (X))) Correction for GeoGebra Script on Android / iOS Zoomin () working for 3D View (Non-dynamic) Add fictitious GGBAPPLET.ISEXERCISE (), which returns false latex: Stretch tables with for example RenewCommand { ArrayStritch} {1,2} and RenewCommand {tabolSEP} {3pt} AR: Create and move Points 3D View: SetViewDirection () now works when the axes ratio is not 1: 1: 1 CAS Vista: correction for SUM (SUM (N * M * (1/2) ^ (N + M), N, 0, A), M, 0, A) CAS Vista: Add sort () and TestDefinito () CAS Vista: Correction for Solveode ( y '= sqrt (x), (1.1)) cas app: support for unfinished variables classic 5: correction for alert () in javascriptfix for example 5 * 10 ^ (- 2) correction for ing to the 3D buttons Zoom: Fix for "ghost" objects G RICA / Geometry: New call API GGBAPPLET.SETPERSPECTIVE () and also notifications from RegisterClientListener () when the user changes the view to Android: improvement for the PlotingCientific function: For the mutual key immediately after a fraction correction for example the 8 best highlighting for the buttons to fix * A (- A) CAS Vista: fixes to resolve ({Exp (x ^ 2 + y ^ 2) = 8, Exp (x ^ 2 + y ^ 2) = 8 * y ^ 2}, {x, y}) and {{-1, -2, -2}, {-i, 1-2?z?, -1-i} , {I, -1 + I, 1 + 2i}} * (1.0.0.0) Android / iOS: "Trace" and "Point Capture" Options AddedClassic 5: correction for large icons Corner tool (-1.13) Returns Scales for X, Y, Z Axis Improvement for F (X) = (3/2) ^ X, F (-1) GeoGebra 6: Make sure more decimal PL Axis (minimum 5) are used when editing the Editor expression : correction for an ? ? immediately after loga a (x) and for example 3 | X | Latex: corrections for example v_ {1} '^ {2} and {@ hspace {3.7 mm}} Geometry: "Fit to to to Preserves proportions New predefined labels for EQ1 equations, EG2, ... CAS Vista: Correction for ES vector [(X, Y, Z)] = Vector [(1,2,3)] Fix Slowplot () GeoGebra 6: Correction problem When the text is re-published (open text window open) missing 180 ? ? solution for nsolutions for example (4 sin?,? (x) so (x) -6cos?,? (x) sin (x)) 3d view : Corner (-1, 12) Display from left to right towards 3D Vista Coordinates Statistics Calculator: Correction for problems entering for example 0.01, 1/60 Consistently Greek character added for fast correction for self-cursor ad Example y = mx + c bug fix with a ((?,?)) for quadratic inequalities graphic representation: "table of values" working for conical for example y = x ^ 2fix missing letter m in Portuguese function keyboard inspector: correction For Min / Max3D View: fixed adjustment / load correction Distances Reticle Correction to reflect (Pendoke, object) Bug FIX: Table View works when embedded CAS Vista: correction to resolve (x ^ 3 + 2x ^ 2 + 15x + 2> 0) (only offline) and numeric ((Exp (-lambertw ((- 1) / 2 LN (2 ), - 1))), 15) Classic 6: Adjust the character size of the CAS properly graphic / geometry: VERT (matrix) AGAINCAS WORK View: numeric correction (0.99999874 Millions ^ 16500) CAS View: correction to solve ({d, and}, {x, y}) and resolve ({d, e, f}, {x, y, z}) where d, e, f are conical / quadrics defined in the keyboard Algebra view: Accents added to the Portuguese keyboard Classic 6 Image Tool: Webcam option works on iOS, and uses the rear camera (where available) correction for character style for labels Editor: Be sure to log_10 is displayed correctly 3D: improvements for creation of solid (create regular 3D view polygons, create square cube, tetrahedron from equilateral polygon, etc.) 3D: STL EXPORT Dialogue Chrome: UpdateMen To Image Tool for New API exam: doing safe exit FitGrowth () is ShownChrome: problem Full-screen correction Modegraphing / Geometry: Table View Safari: Correction Load problem Multiple Safari Activities: Make sure full-screen is resolution Native of the graphic screen / geometry: correction for example length (sqrt (x), 1.4) CAS Vista: Fix bug with quadrics and coefficients (conical / quadrica) works Editor: Correction for example a new algorithm for convexhull ( ) Parallel and perpendicular Line Work tools for linear functions Best highlighting check boxes when they have the Focus Cas Vista: corrections to resolve ({A = A + B * C / (B + C), B = B + A * c / (a ? New 5.0.290.0 ASIND () functions, (), ATAND (), ATAN2D () to return the answer in degrees 3D View: Drag ret to open / close Desktop: correction for in the entry bar CAS View: Complexroot [] modified to give a numerical answer Make sure that the scripts of Run input box in the right order when the button is clicked the Debian repository is signed with SHA512 5.0.289.0 of running away Tool Polylins Fix for Data Analysis View 5.0.288.0 New lines form AX + bY + C = 0 new forms for paraboli (conical shape and vertex Module) CAS View: correction for (x = y) + (x = y) * (- 1) Fixing for Z-test of proportions difference new method for locumuse [] under the hood to add corners, for example ? ? + ? + ? ? + I? + ? 'A + I? 5.0.286.0 Fasteners for input boxes connected to the sliders 3D view: Fixing orientation 5.0.284.0 Vista CAS: correction for nSolve [X ^ 5730 = 1/2] 5.0.283.0 enhancements for 3D polyline solution INVERT [LO G (3, X + 1)], INVERT [LOG (X + 1,3)] 5.0.282.0 Correction Problem with IntersetPath [Polygon, Line] Correction Problem with the input bar Giving error eg. Integral [x, 0,1] logarithmic grid for data analysis (beta) 5.0.281.0 Improvements surd, eg. Simplify [CBRT (X ^ 6)] gives X ^ 2 implicit polynomial curves not 5.0.280.0 results from derivatives and integrals in the cache in the XML cache rapid Trascinzione of CAS functions in the app Web graphics: Print Algebra View and Brush Construction Protocol the pen tool and freeform tool in Move Down the Move tool, text tool Moved CAS View: numerically solve the tool correction for 2 lines \ qquad latex 5.0.279.0 Make sure the order of algebra display is saved / recharged properly 5.0.278.0 Desktop: correction for "Alpha" Popup Web APP: correction for the drag to change the order in the construction protocol Cas View: Fix for Focus Problem (Web) 5.0.277.0 CAS View: correction for nSolve [ (SQRT (3) 4 x ? + 12x? ? - SQRT (3) 12 x-4)] Vista CAS: numerically solve the tool adds initial values for systems of equations, for example, {2.5 = A * B ^ -5, 8.4 = A * B ^ 7} 5.0.276.0 HTML5: Correction for editing in spreadsheet / Old entry bar 5.0.275.0 Vista CAS: correction to simplify [SQRT (2) * SQRT (5)] and solve [(SQRT (3 ) 4 x + ? 12X? - SQRT (3) 12 x - 4)] 5.0.27 4.0 Desktop: fix for the missing language menu 5.0.273.0 View Cas: correction for LN (0) and integral [ABS (x Cos ( X?)), 0, SQRT (PI)] 3D View: Hide slider to export New syntax: SetviewDirection [, ] for example SetviewDirection [Vector [(1; ? ?; ? -30 ?)], false] text tool: paste into formatted text now works (stripped with formatting) correction for the cross product In Editor 5.0.272.0 Fixing for the export of PNG from New 3D view of the app selection solution for ZIP [CustomTool []] Fix a '(T) where a is an improvement of the parametric curve for the 5.0.271.0 design locus drawing for two variable regression tools 5.0 .270.0 Make sure the Polygon segments are correct color after the tablet app of translation: use the native graphing calculator GIAC (TBC) 5.0.269.0: reporting tool implemented export EPS: correction for 'track export and adjust the color according to the background color transparent fills the entire cell in tablet [] Now 5.0.268.0 5.0.266.0 correction \ otimes CAS View: Fix for Translate [ellipse] New methods GGBAPlet API. SetPoi ntcapture ( view, mode), ggbapplet.setaxissteps (view, x, y, z), ggbapplet.setaxislabels (view, x, y, z), ggbapplet.sexisunits (view, x, y, z), ggbapplet.seuxilliary (Geo, TRUE / FALSE) New TableText [] alignment Option "%" to In a percentage and align on decimal points 5.0.265.0 New tablet alignment option [] "." To align the fixed decimal points for loading InterSectPath [] 5.0.264.0 "% 0" replaced by the name of the object in the click scripts and updates 5.0.263.0 Correction for the automatic graphics calculator: correction for the bug editor with ( 1.1 / 2) Examination mode: Make sure that F '(X) works in Non-CAS mode 5.0.262.0 5.0.261.0 Vista CAS: Correction to resolve [(x + 5) * Exp (x) = (x + 5 ) * Exp (2 * x)] Vista CAS: correction for (x Enter more improvements for copy & paste in 3D Chrome App: Correction for displaying complex numbers in the Algebra view 5.0.50.0 HTML5: Correction per click without toolbar 5.0. 49.0 CAS Vista: fixed problem with C_1 changing to C_2 P alternates the probability view Make sure the style bar does not change the probability Calculator allows root [] and extreme [] to If [0 Insert Work Correction File for Right Mouse Right Button in Correction of graphic view for g when a selected polygon angle [(1.2), (3.4)] as a shortcut per angle [vector [(1.2)], vector [(3.4)]] 5.0 .47.0 Chrome app: solution problems with the image by entering from webcam correction for vertical toolbar plus large toolbar icons when enhanced writing magnitude CAS Vista: correction for derivative [1] Open object properties -> Make sure that all selected objects remain selects TI 5.0.46.0 (iOS app) app) For c == f per line, function function correction guide for custom tools mac os: interpret 0 (zero) as a degree of correction of the degree symbol with the relative copy with condition to view other improvements for exporting PSTRICKS / PGF / ASYMPTOTE 5.0. 45.0 5.0.44.0 Fixing for the turtle position on loading File Vista CAS: Correction to obtain for example 4.35372862870553E8 From Algebra View App Chrome: Make sure the rectangle selection functions when the toolbar Show 5.0.42.0 Fix for F == G (for multilive functions) and to intersect [curve, curve] Triangular correction [0, 50, 25, X, false] New version of GIAC with correction for integral [(X-2) (X-3)) ^ 2,2,3] 5.0.39.0 New Command Polar [, ] To find the pole of a line Allow the transparent SVG export fastening problem with a relative copy of SE [ 0

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